Basic Math Examples

\sqrt{50} + \sqrt{128}

$\sqrt{50} + \sqrt{128}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

50

$50$ as

5^{2} \cdot 2

$5^{2} \cdot 2$ .

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Step 1.1.1

Factor

25

$25$ out of

50

$50$ .

\sqrt{25 (2)} + \sqrt{128}

$\sqrt{25 (2)} + \sqrt{128}$

Step 1.1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\sqrt{5^{2} \cdot 2} + \sqrt{128}

$\sqrt{5^{2} \cdot 2} + \sqrt{128}$

\sqrt{5^{2} \cdot 2} + \sqrt{128}

$\sqrt{5^{2} \cdot 2} + \sqrt{128}$

Step 1.2

Pull terms out from under the radical.

5 \sqrt{2} + \sqrt{128}

$5 \sqrt{2} + \sqrt{128}$

Step 1.3

Rewrite

128

$128$ as

8^{2} \cdot 2

$8^{2} \cdot 2$ .

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Step 1.3.1

Factor

64

$64$ out of

128

$128$ .

5 \sqrt{2} + \sqrt{64 (2)}

$5 \sqrt{2} + \sqrt{64 (2)}$

Step 1.3.2

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

5 \sqrt{2} + \sqrt{8^{2} \cdot 2}

$5 \sqrt{2} + \sqrt{8^{2} \cdot 2}$

5 \sqrt{2} + \sqrt{8^{2} \cdot 2}

$5 \sqrt{2} + \sqrt{8^{2} \cdot 2}$

Step 1.4

Pull terms out from under the radical.

5 \sqrt{2} + 8 \sqrt{2}

$5 \sqrt{2} + 8 \sqrt{2}$

5 \sqrt{2} + 8 \sqrt{2}

$5 \sqrt{2} + 8 \sqrt{2}$

Step 2

Add

5 \sqrt{2}

$5 \sqrt{2}$ and

8 \sqrt{2}

$8 \sqrt{2}$ .

13 \sqrt{2}

$13 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

13 \sqrt{2}

$13 \sqrt{2}$

Decimal Form:

18.38477631 \dots

$18.38477631 \dots$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$